Question : Three circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?

Option 1: $36 + 12\pi\ \text{cm}$

Option 2: $36 + 18\pi\ \text{cm}$

Option 3: $24 + 36\pi\ \text{cm}$

Option 4: $36 + 20\pi\ \text{cm}$

Question : Two equal circles of radius 18 cm intersect each other, such that each passes through the centre of the other. The length of the common chord is ______.

Option 1: $6 \sqrt{27}\ \text{cm}$

Option 2: $9 \sqrt{27}\ \text{cm}$

Option 3: $\sqrt{3}\ \text{cm}$

Option 4: $3 \sqrt{3}\ \text{cm}$

Question : There are two circles which touch each other externally. The radius of the first circle with centre O is 17 cm and the radius of the second circle with centre A is 7 cm. BC is a direct common tangent to these two circles, where B and C are points on the circles with centres O and A, respectively. The length of BC is:

Option 1: $2 \sqrt{118} $ cm

Option 2: $2 \sqrt{119} $ cm

Option 3: $2 \sqrt{113} $ cm

Option 4: $2 \sqrt{117}$ cm

Question : Two circles with radii $22 \ \text{cm}$ and $16\  \text{cm}$ touch each other externally. The length of the direct common tangent is:

Option 1: $4 \sqrt{22}\ \text{cm}$

Option 2: $8 \sqrt{11} \ \text{cm}$

Option 3: $4 \sqrt{11} \ \text{cm}$

Option 4: $8 \sqrt{22} \ \text{cm}$

Question : The length of a side of an equilateral triangle is 8 cm. The area of the region lying between the circumcircle and the incircle of the triangle is __________ ( Use: $\pi = \frac{22}{7}$)

Option 1: $50\frac{1}{7}\ \text{cm}^2$

Option 2: $50\frac{2}{7}\ \text{cm}^2$

Option 3: $75\frac{1}{7}\ \text{cm}^2$

Option 4: $75\frac{2}{7}\ \text{cm}^2$